There are references to rasis in the balakanda : तत: then, यज्ञे when sacrifice, समाप्ते was completed, ऋतूनाम् of seasons, षट् six, समत्ययु: were spent, तत: then, द्वादशे मासे in twelfth month, चैत्रे in Chaitra month, नावमिके तिथौ on the nineth day of the rising Moon, अदितिदैवत्ये presided by Aditi as devata, नक्षत्रे when the star (Punarvasu) , पञ्चसु ग्रहेषु and the five grahas, स्वोच्चसंस्थेषु in their own exalted places (houses), कर्कटे लग्ने in Karkata Lagna, वाक्पतौ when Brihaspati, इन्दुना सह along with Moon, प्रोद्यमाने was rising, कौसल्या Kausalya, जगन्नाथम् lord of the entire universe, सर्वलोकनमस्कृतम् bowed to by all the worlds, सर्वलक्षणसंयुतम् adorned with all the characteristics, विष्णो: Vishnu’s, अर्धम् facet, महाभागम् highly fortunate, ऐक्ष्वाकुवर्धनम् perpetuating the Ikshvaku race, रामम् Rama, पुत्रम् as his son, अजनयत् gave birth . ” Source

Note that there is a mention of grahas (पञ्चसु ग्रहेषु) and of rasis (कर्कटे लग्ने) but the naksharadhipati was Aditi : “अदितिदैवत्ये नक्षत्रे when the nakshatra presided by Aditi as devata”

Dasaratha, Kausalya and their sons were always compared to Vedic Deities such as Indra, Aditi, Yama, Varuna etc.

Contemporary Hindu Astrology : This ascribes the adhipatyam (lordship) of the Nakshatras to Grahas. The vimsottari dasa calculations are based on this. This probably happened when the brihat parasara hora sastra became popular. This sastra was taught by Veda Vyasa’s father, Parasara to Maitreya. By Valmiki’s time, it may have been just beginning to gain acceptance. Valmiki and Vyasa were contemporaries, with Valmiki somewhat older to Vyasa. See (Generations between Rama and Krishna.)

Note: The muhurta selection, in the Ramayana was done by the kings themselves and not their priests and the muhurtam was sun-rise in both cases. Nowadays, the muhurta is selected any time of the day or night. It may also be noted that then a muhurta was a time unit of 48 min duration, but many modern Hindu weddings have to be performed at an exact instant, which is labelled the muhurtam.